{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Practical Statistics for Data Scientists (R)\n",
    "# Chapter 2. Data and Sampling Distributions\n",
    "> (c) 2019 Peter C. Bruce, Andrew Bruce, Peter Gedeck"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import required R packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Registered S3 methods overwritten by 'ggplot2':\n",
      "  method         from \n",
      "  [.quosures     rlang\n",
      "  c.quosures     rlang\n",
      "  print.quosures rlang\n"
     ]
    }
   ],
   "source": [
    "library(boot)\n",
    "library(ggplot2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define paths to data sets. If you don't keep your data in the same directory as the code, adapt the path names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "PSDS_PATH <- file.path(dirname(dirname(getwd())))\n",
    "\n",
    "loans_income <- read.csv(file.path(PSDS_PATH, 'data', 'loans_income.csv'))[,1]\n",
    "sp500_px <- read.csv(file.path(PSDS_PATH, 'data', 'sp500_data.csv.gz'), row.names=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 2.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>null device:</strong> 1"
      ],
      "text/latex": [
       "\\textbf{null device:} 1"
      ],
      "text/markdown": [
       "**null device:** 1"
      ],
      "text/plain": [
       "null device \n",
       "          1 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<strong>null device:</strong> 1"
      ],
      "text/latex": [
       "\\textbf{null device:} 1"
      ],
      "text/markdown": [
       "**null device:** 1"
      ],
      "text/plain": [
       "null device \n",
       "          1 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iDtcUfEn7rt96hIPQ4BAgQIECBAgACB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\nDdmsv2X4W/sAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- seq(from=-3, to=3, length=300)\n",
    "gauss <- dnorm(x)\n",
    "\n",
    "    par(mar=c(3, 3, 0, 0)+.1)\n",
    "    plot(x, gauss, type='l', col='blue', xlab='', ylab='', axes=FALSE)\n",
    "    polygon(x, gauss, col='blue')\n",
    "dev.off()\n",
    "\n",
    "    norm_samp <- rnorm(100)\n",
    "    par(mar=c(3, 3, 0, 0)+.1)\n",
    "    hist(norm_samp, axes=FALSE, col='red', main='')\n",
    "dev.off()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sampling Distribution of a Statistic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# take a simple random sample\n",
    "samp_data <- data.frame(income=sample(loans_income, 1000), \n",
    "                        type='data_dist')\n",
    "\n",
    "# take a sample of means of 5 values\n",
    "samp_mean_05 <- data.frame(\n",
    "  income = tapply(sample(loans_income, 1000*5), \n",
    "                  rep(1:1000, rep(5, 1000)), FUN=mean),\n",
    "  type = 'mean_of_5')\n",
    "\n",
    "# take a sample of means of 20 values\n",
    "samp_mean_20 <- data.frame(\n",
    "  income = tapply(sample(loans_income, 1000*20), \n",
    "                  rep(1:1000, rep(20, 1000)), FUN=mean),\n",
    "  type = 'mean_of_20')\n",
    "\n",
    "# bind the data.frames and convert type to a factor\n",
    "income <- rbind(samp_data, samp_mean_05, samp_mean_20)\n",
    "income$type <- factor(income$type, \n",
    "                     levels=c('data_dist', 'mean_of_5', 'mean_of_20'),\n",
    "                     labels=c('Data', 'Mean of 5', 'Mean of 20'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EDAioBO6Rlv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\nVJ3l7rjjjjN/48ePt82JESTbKMkIA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AACCCCAQNwKECDFbdfSMAQQ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\nh0MAAQQQQAABBBBAAAHnCvw/Omkfyjj02M0AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(income, aes(x=income)) +\n",
    "  geom_histogram(bins=40) +\n",
    "  facet_grid(type ~ .)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Bootstrap\n",
    "As the calculation uses random samples, results will vary between runs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "ORDINARY NONPARAMETRIC BOOTSTRAP\n",
       "\n",
       "\n",
       "Call:\n",
       "boot(data = loans_income, statistic = stat_fun, R = 1000)\n",
       "\n",
       "\n",
       "Bootstrap Statistics :\n",
       "    original   bias    std. error\n",
       "t1*    62000 -65.0535     203.111"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stat_fun <- function(x, idx) median(x[idx])\n",
    "boot_obj <- boot(loans_income, R=1000, statistic=stat_fun)\n",
    "\n",
    "boot_obj"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Confidence Intervals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>ci</th><th scope=col>y</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>51643.09</td><td> 9      </td></tr>\n",
       "\t<tr><td>65262.95</td><td>11      </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " ci & y\\\\\n",
       "\\hline\n",
       "\t 51643.09 &  9      \\\\\n",
       "\t 65262.95 & 11      \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| ci | y |\n",
       "|---|---|\n",
       "| 51643.09 |  9       |\n",
       "| 65262.95 | 11       |\n",
       "\n"
      ],
      "text/plain": [
       "  ci       y \n",
       "1 51643.09  9\n",
       "2 65262.95 11"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QEJaJAGxOYgAgQIECBAgAABAgSyKKBB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\n+C9NkR3UpE92UAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# R version for figure 2-9 not available\n",
    "set.seed(5)\n",
    "set.seed(7)\n",
    "sample20 <- sample(loans_income, 20)\n",
    "sampleMean <- mean(sample20)\n",
    "\n",
    "stat_fun <- function(x, idx) mean(x[idx])\n",
    "boot_obj <- boot(sample20, R=500, statistic=stat_fun)\n",
    "boot_ci <- boot.ci(boot_obj, conf=0.9, type='basic')\n",
    "X <- data.frame(mean=boot_obj$t)\n",
    "ci90 <- boot_ci$basic[4:5]\n",
    "ci <- data.frame(ci=ci90, y=c(9, 11))\n",
    "# ci <- boot_ci$basic[4:5]\n",
    "ci\n",
    "ggplot(X, aes(x=mean)) +\n",
    "    geom_histogram(bins=40, fill='#AAAAAA') +\n",
    "    geom_vline(xintercept=sampleMean, linetype=2) +\n",
    "    geom_path(aes(x=ci, y=10), data=ci, size=2) +\n",
    "    geom_path(aes(x=ci90[1], y=y), data=ci, size=2) +\n",
    "    geom_path(aes(x=ci90[2], y=y), data=ci, size=2) +\n",
    "    geom_text(aes(x=sampleMean, y=20, label='Sample mean'), size=6) +\n",
    "    geom_text(aes(x=sampleMean, y=8, label='90% interval'), size=6) +\n",
    "    theme_bw() + \n",
    "    labs(x='', y='Counts')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Normal Distribution\n",
    "## Standard Normal and QQ-Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QUUWBSBiRMnfo3P30iunTp16vZDhw59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\nwE8FRo8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      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "norm_samp <- rnorm(100)\n",
    "qqnorm(norm_samp, main='', xlab='Quantile of normal distribution', ylab='z-score')\n",
    "abline(a=0, b=1, col='grey')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Long-Tailed Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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j8KCCCAAAIIIIAAAggggEAkQIHEjwICCCCAAAIIIIAAAgggEAlQIPGjgAACCCCA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uUB5WaAgggAACJRTQdxW16dmzZx8dcrie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\nEEAAAQQQQKDcBCiQyu0T4XwQQAABBBBAAAEEEECgxQQokFqMngMjgAACCCC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fd8\n6j3xz+1zLR+c5X5aYrNsnLdKXduFLXGCHBMBBBAoR4G25XhSnBMCCCCQYIF5urZDYte3qV4f\npzys3BRb96Jed4ktq/SX43UB7WMX4et00VLM3qPYIZt8uYO2uFvppNyo3K68oqyn/ELZT7lO\ncQ/fWKXcWqU4l5sb54MAAggggAACCCDQwgLuJXLvxJ8znEfSepDe0nW+n+Fai7042x4kF6U+\nxwXKPhlOan0t/0r5Ttk5wzYtuTgbZ3qQWvIT4tgIIFCWAvQgleXHwkkhgAACGQU6a40Lqp7K\nVOUR5TUl3vzn+x7Kxopv65ukuDdkthJvdVrQV/HtZG6TlXuUb/0i0n6ueT+z4v0cqiyl/J/i\nXhW3po65uLbpo3haqxysvKs8rmyvrKq4l2aOEpr3uZni3pwuip/Bcm+Ne+KibWm92FFZR/F2\n/1aeVLx9Pu1IvcnPG7lHz7f/pWt276c8pLgnaVVloeJzsb1dJirR5meA3AN1l/JlZEU252/7\nvZRnlI+VXZXNlU8Un0O41nyc9fYftbW0xJ+5TacqjyrhGJr9b1tec/2VNZRPlVeVe5UGhYYA\nAggggAACCCCAQM4CvfUO/2L95wzv7JFa796P11Pz7rXwe/xLqH85jbbV9eI5xeu/VvysjOf9\nC733FW2b6IV7Grz+G8Xbe97L/Mt8tLkwek/xeXobx7+Yu2VzTP/C7R6Z8F7P36q4uQjx8m5+\nkWoudF5WvNznNiM17+uI3qK3t15/llrn83eB5fd4EIahSrTZ0Os6RBemmX8ptd26adbFFwU/\nDwDhtpXiY1zoF7F2uV57nQvc0LI9//BzcK7e6CLE+/EtiZ7OU1zUueXinOlcT9J+/DPmz8g9\naf45s+fvlNZKaDtpJnj75yz8XL6g+RXDRkwRQAABBBBAAAEEEMhFINsCyb8I1ysuRlwgDFT8\nS6sLh/BLq6f+5dTLB0WW76z5L5R/Ke4xcnOR8IYyU9lPaaP4/X0VFyQfKosrod2tGf+i/KVy\nuLK/8jMll2Nq80XFl3/pjrZ4gdROKx9X/Mt3uA6f7zDFDqcrbj4/n6uvbTOlRumk2NS/rH+r\nLKGEdr9m/P7GCiTvw9fposM9WE2127WB93lUasOtUq8vTL2OTuIFUi7n3yO1Xxct7kXbWvH5\nucDytU5XOiqhvaWZppzTnesv9T5fz2PKCorbYsotipcfrIT2jmY+U9ZPLXAPp4sob3dBahkT\nBBBAAAEEEEAAAQRyEsi2QJqmvUZ7TnyQJxX/MrqyX6jtp/i1i5l4O1cLvG5IasUJqddnpl5H\nJyem1p0dWeh9+v2/jizzbC7H9PbZ/OLugs7H+qPfEGkuxh5WHlRqFf+Cf79ymBJv4Xw3jKzw\ntt5vYwXS8qlt/h15X2Ozp6S2Py+1kc/Jx8imQPK2Pqdszj8USFO1fShyNbuouWDyMb1NaNk4\npzvXN7QD7+snYUepqQtPF5wfKf4c/LPoQvxRxa9Dc3F7qrJbWMAUAQQQqCSBbP5lrJKuh3NF\nAAEEkiwwWRc3J3aBj+r1tsrqigso/8Lr9g8l+suyl/nWNDf3tIxUevqF2pjvJz/47816dani\nbePtudiCXI4Ze2vGl5uk1tTHtvAv7jtGlj2r+V9EXrtoWkPZWPH3HblFe1W+X9L4f90b4+aC\nIJsWii33YuXa8jn/iTqIb62LtqmpF4tHF+Yx30XvWUdxcTVPif8MvaBlP1Pcs/Sh8pSyvfK0\n4iLtfsW3gf5BoSGAAAIVKUCBVJEfGyeNAAJVKuACKN7CL/M1qRVrpaaXxTeMvF4zNe9fhF1w\nvB9ZF2Y/1cxsJWwblnv6bvSF5nM5ZuytGV+G4i3ducXf5HM8SemleL6tskCZobhFeze+X9L4\nf6drta99OcW3jPkWxMbauqmVrzS2USPrcj3/j9Psa05qWZs063JZFD5LT12QZ2o+5w+V/spt\nyg6KC2X/3Pnn40bl90q8kNMiGgIIIFDeAv5LhIYAAgggUBkC/qW/qRZ+UT5AG36SYWM/s+M2\nS3Hx4B4Q9xZEW51etFfC/qLr4r/0hm2yOWZ0P43Nh/NpqvfHxYl7L/yMzAPKTcokxT0dw5Wj\nlXyab+PbU/mpcl8jO/Dfo6GX7f/bubeQy8Y4DOByiKTRhEgh5yJDIcMNOXPhcONQipTkAiWH\ncpooJG6ESA4RbpwliZJQlCjlBklKDiGU5AJ5Ht9e05rdZ8/eMjH5/ev51lrvWnutd/2+ffG+\ns9Y3/Y8TxrXcxKwTrnH9nf7P8z0YX2OR9eF3WcvbZnxwmAx2In10sk9yUnJiclSyJjk8OSFR\nBAgQ2KgETJA2ql+XzhIgQGC9Ah9NjugkqIP8cfX1qQ7mv5o0fpzlMcl+yduTtmHRgXsH+J8N\nDTOWi1xzxmnW2TX8/c+eaR1eDRwOuDIrq5PLk0uSlcl5ycPJuDpob222tFjo5wM5uhOkW5OX\nk9+SVs/VCdPdyXPJFckek/Uvs2wNk4ytljbX+bnXOlsbrv9Tl5l7s+59qrh9Mv396UkOS2rR\np3N9BbGvQn6TfJj0e3BHsl3yfnJ8snPyRaIIECCw0QhsutH0VEcJECBAYB6B53NQB7hXJ9MT\ng7vS9krSf9lvPbu0+PMP6qefdvTzrWeWFjN/LnLNnqhPhzq4nlUvZmfv4+Kpg1Zk+5rk2KSv\neO2etD5dWqz92YH7cJ9brG2df6U2NyUHJI8l2yatlUn/cbH730vWJN8nFyVDfTtZ6d/qjH8H\nPdfBk32D94bqfy8zj/OkO2sXfbXw5aT9PHlt69LK/lm8nnTy2N9NJ3tvJI8m4/ouG58lnUgN\nk8XxfusECBAgQIAAAQIEZgqclr0dcHYCs1ytSmP337nMzusm+44Z7Xtw0vZmlmcmpycPT9qe\ny3JcT2ej534h6XGnJkPbfVkfBvJZ/fN/xuuxK7oxVYtc87V8tud5KDk/aT2RtG2Hbkzq/izb\n1j6fklyYvJO07ZKk1Sc43X43OTs5Irkq+SbpQL37el9DvZSVtvW1wnnqnhzU4z9P2p9Lk1uS\nT5O2N50sTZ/vrdG+c7J+Q9InKX3S0s8clLQW6f+qHN/PLvc9uHGyr5OyoV7LSo9/KPkr5z6J\n6zF9UjbUvlnpRKlZkxyX9Kldny79mhySDPVqVvr5GpybnJE8krTtqUQRIECAAAECBAgQWFjg\nn54gbZoedOD9Q9KBavN78mSyUzKuPl3p4PqnZDi2A+Gbk/HkKJszJ0iLXPPInOvrpNf7IGkt\nN0Hq05drk3Hf+rTm4mSoHtNJTAfuQ//7CuEFSQfybbs3GWrRCVLv67Lkk2Q4f5c/J5103p78\nknQCdVYy1G5ZeT0ZPvNj1q9Pzp+0HZhla5H+LzpBOjLnX5/z6hzTPo4nSNncpK9Ytv99CjTc\nQ+/x3GRc22Xj8WTs39c770r63VIECBAgQIAAAQIE/lMCu6Y3HYyvWE+vOhnaM9llPcfNs3ve\na+6Yky33dzrT1+gkZa+kTzY2n9452e799anMzn+x/59o3iknOTRpX7YcnXD3rHfy2UnldK1M\nw/5JJ0KzakP2f17n5fq3dRrrulsy6x62yf7e597J9MQ6TYoAAQIECBAgQIAAgf+bwKwJxP/N\nwv0SIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAIF/\nX+AP7b/uzafkPWoAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “Normal Q-Q Plot”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nflx <- sp500_px[,'NFLX']\n",
    "nflx <- diff(log(nflx[nflx>0]))\n",
    "qqnorm(nflx)\n",
    "abline(a=0, b=1, col='grey')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binomial Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0729"
      ],
      "text/latex": [
       "0.0729"
      ],
      "text/markdown": [
       "0.0729"
      ],
      "text/plain": [
       "[1] 0.0729"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dbinom(x=2, size=5, p=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.99144"
      ],
      "text/latex": [
       "0.99144"
      ],
      "text/markdown": [
       "0.99144"
      ],
      "text/plain": [
       "[1] 0.99144"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pbinom(2, 5, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0175879466057216"
      ],
      "text/latex": [
       "0.0175879466057216"
      ],
      "text/markdown": [
       "0.0175879466057216"
      ],
      "text/plain": [
       "[1] 0.01758795"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dbinom(x=0, size=200, p=0.02)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Poisson and Related Distribution\n",
    "## Poisson Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>1</li>\n",
       "\t<li>3</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>5</li>\n",
       "\t<li>4</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>2</li>\n",
       "\t<li>6</li>\n",
       "\t<li>1</li>\n",
       "\t<li>5</li>\n",
       "\t<li>6</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "\t<li>3</li>\n",
       "\t<li>0</li>\n",
       "\t<li>2</li>\n",
       "\t<li>6</li>\n",
       "\t<li>5</li>\n",
       "\t<li>2</li>\n",
       "\t<li>4</li>\n",
       "\t<li>1</li>\n",
       "\t<li>0</li>\n",
       "\t<li>2</li>\n",
       "\t<li>0</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>5</li>\n",
       "\t<li>3</li>\n",
       "\t<li>1</li>\n",
       "\t<li>4</li>\n",
       "\t<li>4</li>\n",
       "\t<li>4</li>\n",
       "\t<li>0</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>0</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>4</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>4</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>1</li>\n",
       "\t<li>4</li>\n",
       "\t<li>0</li>\n",
       "\t<li>3</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>0</li>\n",
       "\t<li>3</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>0</li>\n",
       "\t<li>3</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>4</li>\n",
       "\t<li>0</li>\n",
       "\t<li>2</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>0</li>\n",
       "\t<li>1</li>\n",
       "\t<li>3</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>1</li>\n",
       "\t<li>4</li>\n",
       "\t<li>0</li>\n",
       "\t<li>3</li>\n",
       "\t<li>6</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 5\n",
       "\\item 4\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 2\n",
       "\\item 6\n",
       "\\item 1\n",
       "\\item 5\n",
       "\\item 6\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\item 3\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 6\n",
       "\\item 5\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 1\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 5\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 4\n",
       "\\item 4\n",
       "\\item 4\n",
       "\\item 0\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 4\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 4\n",
       "\\item 0\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 0\n",
       "\\item 3\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 0\n",
       "\\item 3\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 4\n",
       "\\item 0\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 0\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 4\n",
       "\\item 0\n",
       "\\item 3\n",
       "\\item 6\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 2\n",
       "3. 1\n",
       "4. 3\n",
       "5. 2\n",
       "6. 2\n",
       "7. 2\n",
       "8. 5\n",
       "9. 4\n",
       "10. 1\n",
       "11. 2\n",
       "12. 3\n",
       "13. 2\n",
       "14. 6\n",
       "15. 1\n",
       "16. 5\n",
       "17. 6\n",
       "18. 2\n",
       "19. 3\n",
       "20. 1\n",
       "21. 1\n",
       "22. 1\n",
       "23. 1\n",
       "24. 1\n",
       "25. 3\n",
       "26. 4\n",
       "27. 3\n",
       "28. 0\n",
       "29. 2\n",
       "30. 6\n",
       "31. 5\n",
       "32. 2\n",
       "33. 4\n",
       "34. 1\n",
       "35. 0\n",
       "36. 2\n",
       "37. 0\n",
       "38. 2\n",
       "39. 3\n",
       "40. 5\n",
       "41. 3\n",
       "42. 1\n",
       "43. 4\n",
       "44. 4\n",
       "45. 4\n",
       "46. 0\n",
       "47. 3\n",
       "48. 3\n",
       "49. 2\n",
       "50. 2\n",
       "51. 0\n",
       "52. 2\n",
       "53. 2\n",
       "54. 4\n",
       "55. 1\n",
       "56. 1\n",
       "57. 3\n",
       "58. 3\n",
       "59. 3\n",
       "60. 4\n",
       "61. 2\n",
       "62. 3\n",
       "63. 3\n",
       "64. 1\n",
       "65. 1\n",
       "66. 2\n",
       "67. 1\n",
       "68. 2\n",
       "69. 3\n",
       "70. 1\n",
       "71. 4\n",
       "72. 0\n",
       "73. 3\n",
       "74. 1\n",
       "75. 2\n",
       "76. 0\n",
       "77. 3\n",
       "78. 2\n",
       "79. 3\n",
       "80. 0\n",
       "81. 3\n",
       "82. 1\n",
       "83. 2\n",
       "84. 2\n",
       "85. 4\n",
       "86. 0\n",
       "87. 2\n",
       "88. 1\n",
       "89. 2\n",
       "90. 3\n",
       "91. 0\n",
       "92. 1\n",
       "93. 3\n",
       "94. 2\n",
       "95. 2\n",
       "96. 1\n",
       "97. 4\n",
       "98. 0\n",
       "99. 3\n",
       "100. 6\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  [1] 1 2 1 3 2 2 2 5 4 1 2 3 2 6 1 5 6 2 3 1 1 1 1 1 3 4 3 0 2 6 5 2 4 1 0 2 0\n",
       " [38] 2 3 5 3 1 4 4 4 0 3 3 2 2 0 2 2 4 1 1 3 3 3 4 2 3 3 1 1 2 1 2 3 1 4 0 3 1\n",
       " [75] 2 0 3 2 3 0 3 1 2 2 4 0 2 1 2 3 0 1 3 2 2 1 4 0 3 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rpois(100, lambda=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exponential Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\\begin{enumerate*}\n",
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       "\\end{enumerate*}\n"
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      "text/markdown": [
       "1. 6.6387056976319\n",
       "2. 0.00671107089146972\n",
       "3. 15.8785874388161\n",
       "4. 6.38528264166629\n",
       "5. 8.68918771813524\n",
       "6. 0.274932847301402\n",
       "7. 1.06028521491309\n",
       "8. 6.01590430343008\n",
       "9. 0.0938750174827874\n",
       "10. 6.455080602108\n",
       "11. 5.10756899318257\n",
       "12. 0.109575668516709\n",
       "13. 1.76504792412743\n",
       "14. 4.22755784334099\n",
       "15. 2.73555422724424\n",
       "16. 2.99772624107118\n",
       "17. 10.1910778410257\n",
       "18. 4.24046883338547\n",
       "19. 5.38781171643591\n",
       "20. 1.49715713458136\n",
       "21. 7.57909522512741\n",
       "22. 5.56268148908022\n",
       "23. 0.48676422405141\n",
       "24. 6.09078133457756\n",
       "25. 6.68753373415625\n",
       "26. 11.2692872335421\n",
       "27. 0.240654313408696\n",
       "28. 0.93524647863907\n",
       "29. 0.237767025828362\n",
       "30. 2.17688306933269\n",
       "31. 4.11088208646929\n",
       "32. 5.98701289368278\n",
       "33. 3.27576701529324\n",
       "34. 2.44518182369098\n",
       "35. 2.65118177514523\n",
       "36. 6.89840606392777\n",
       "37. 19.0709319597029\n",
       "38. 4.2481197921539\n",
       "39. 0.343186936452641\n",
       "40. 12.4508189869331\n",
       "41. 2.6477911563808\n",
       "42. 10.9372709208196\n",
       "43. 0.721764060341698\n",
       "44. 2.24458673556056\n",
       "45. 3.63028225540078\n",
       "46. 6.02424021789289\n",
       "47. 6.94234882740921\n",
       "48. 3.90822082271284\n",
       "49. 1.47203455446288\n",
       "50. 3.39078255929053\n",
       "51. 2.43980085477233\n",
       "52. 37.5974821092045\n",
       "53. 4.77533383739597\n",
       "54. 11.1677639832007\n",
       "55. 8.94654936641915\n",
       "56. 7.29937603655172\n",
       "57. 12.1011851628529\n",
       "58. 3.0562479631044\n",
       "59. 4.74031542406833\n",
       "60. 4.89552368854588\n",
       "61. 1.62813091390937\n",
       "62. 24.5761018324841\n",
       "63. 16.3374472028556\n",
       "64. 7.1010031654349\n",
       "65. 14.9024343879204\n",
       "66. 3.73627926008094\n",
       "67. 8.33818527665312\n",
       "68. 7.30655012610269\n",
       "69. 9.61141072171641\n",
       "70. 5.0246896970174\n",
       "71. 0.56829016949424\n",
       "72. 2.56963648600504\n",
       "73. 2.46017653727904\n",
       "74. 11.7490146582233\n",
       "75. 3.95642243770367\n",
       "76. 2.44337729178369\n",
       "77. 9.85450135501933\n",
       "78. 6.62140896286489\n",
       "79. 2.37537440145388\n",
       "80. 13.8170197320389\n",
       "81. 3.08518774704097\n",
       "82. 1.72244070330635\n",
       "83. 0.445838205571774\n",
       "84. 3.26657653786242\n",
       "85. 4.10568973965607\n",
       "86. 1.33629720053316\n",
       "87. 4.05508079079396\n",
       "88. 1.76590585149825\n",
       "89. 3.5914235193441\n",
       "90. 2.463207191322\n",
       "91. 0.0122641150969449\n",
       "92. 3.26816772576421\n",
       "93. 0.385862767880727\n",
       "94. 3.17886889711023\n",
       "95. 0.920671530423423\n",
       "96. 1.34112713625655\n",
       "97. 0.0603274325840175\n",
       "98. 2.97972794855013\n",
       "99. 3.78438647349781\n",
       "100. 0.993724381551147\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  [1]  6.638705698  0.006711071 15.878587439  6.385282642  8.689187718\n",
       "  [6]  0.274932847  1.060285215  6.015904303  0.093875017  6.455080602\n",
       " [11]  5.107568993  0.109575669  1.765047924  4.227557843  2.735554227\n",
       " [16]  2.997726241 10.191077841  4.240468833  5.387811716  1.497157135\n",
       " [21]  7.579095225  5.562681489  0.486764224  6.090781335  6.687533734\n",
       " [26] 11.269287234  0.240654313  0.935246479  0.237767026  2.176883069\n",
       " [31]  4.110882086  5.987012894  3.275767015  2.445181824  2.651181775\n",
       " [36]  6.898406064 19.070931960  4.248119792  0.343186936 12.450818987\n",
       " [41]  2.647791156 10.937270921  0.721764060  2.244586736  3.630282255\n",
       " [46]  6.024240218  6.942348827  3.908220823  1.472034554  3.390782559\n",
       " [51]  2.439800855 37.597482109  4.775333837 11.167763983  8.946549366\n",
       " [56]  7.299376037 12.101185163  3.056247963  4.740315424  4.895523689\n",
       " [61]  1.628130914 24.576101832 16.337447203  7.101003165 14.902434388\n",
       " [66]  3.736279260  8.338185277  7.306550126  9.611410722  5.024689697\n",
       " [71]  0.568290169  2.569636486  2.460176537 11.749014658  3.956422438\n",
       " [76]  2.443377292  9.854501355  6.621408963  2.375374401 13.817019732\n",
       " [81]  3.085187747  1.722440703  0.445838206  3.266576538  4.105689740\n",
       " [86]  1.336297201  4.055080791  1.765905851  3.591423519  2.463207191\n",
       " [91]  0.012264115  3.268167726  0.385862768  3.178868897  0.920671530\n",
       " [96]  1.341127136  0.060327433  2.979727949  3.784386473  0.993724382"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rexp(n=100, rate=.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Weibull Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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       "\\begin{enumerate*}\n",
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       "\\end{enumerate*}\n"
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       "1. 4499.9469087383\n",
       "2. 4042.55633497126\n",
       "3. 1073.1495671654\n",
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       "5. 4974.52614176412\n",
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       "27. 3278.29462985983\n",
       "28. 5831.18829924818\n",
       "29. 1897.10729386551\n",
       "30. 2874.14050863636\n",
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       "32. 6936.28368575503\n",
       "33. 11993.7818702942\n",
       "34. 2089.01149696554\n",
       "35. 11197.4556462157\n",
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       "59. 72.8318973649935\n",
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       "62. 4862.73786415366\n",
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       "64. 6005.34245824658\n",
       "65. 3371.31646516406\n",
       "66. 3218.09008172202\n",
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       "69. 2220.93148180153\n",
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       "71. 4895.80629989815\n",
       "72. 8644.01646704474\n",
       "73. 762.540326320649\n",
       "74. 3827.43172604326\n",
       "75. 1314.12319094317\n",
       "76. 874.476199379994\n",
       "77. 564.998428652256\n",
       "78. 6972.12479399578\n",
       "79. 4515.33025707628\n",
       "80. 4234.61356418928\n",
       "81. 7463.38093277952\n",
       "82. 1168.32630799661\n",
       "83. 2127.94007122508\n",
       "84. 3922.45391910682\n",
       "85. 15338.53704693\n",
       "86. 3636.37104394751\n",
       "87. 4700.73706406616\n",
       "88. 3738.2288938485\n",
       "89. 3649.29651590692\n",
       "90. 3075.87357309704\n",
       "91. 4767.1116677551\n",
       "92. 7382.92514217553\n",
       "93. 1862.74043248913\n",
       "94. 1723.93241869719\n",
       "95. 5358.53673763179\n",
       "96. 3783.55273200043\n",
       "97. 1631.6235037063\n",
       "98. 9452.39344248378\n",
       "99. 5725.83423782393\n",
       "100. 5672.22971901444\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  [1]  4499.9469  4042.5563  1073.1496  3159.0999  4974.5261  2949.6250\n",
       "  [7]  2128.0114  2405.7802  1436.2068   990.8704 15948.7863  2193.5512\n",
       " [13]   431.2380  8021.5171  7176.8527  1726.1685 15432.2320  3722.5258\n",
       " [19]  2315.5834  4688.6165  5773.7101  5957.3862  4420.9181 11118.2133\n",
       " [25]  5644.0183   268.1725  3278.2946  5831.1883  1897.1073  2874.1405\n",
       " [31]  3694.6321  6936.2837 11993.7819  2089.0115 11197.4556  8322.2591\n",
       " [37]  2814.7802   814.7315 10274.4828  2555.7808  3194.2294  5561.8328\n",
       " [43]  5051.0215  2202.9072  1804.1324  2940.9301  9353.6981 10680.6408\n",
       " [49] 14120.9182  4105.9855  4906.5105  6699.0250  3972.1596  8777.2478\n",
       " [55]  4070.6581   402.4620  1870.7039  4313.7891    72.8319  8042.1638\n",
       " [61]  2897.0133  4862.7379  6869.3911  6005.3425  3371.3165  3218.0901\n",
       " [67]   998.1284   757.3426  2220.9315   275.2842  4895.8063  8644.0165\n",
       " [73]   762.5403  3827.4317  1314.1232   874.4762   564.9984  6972.1248\n",
       " [79]  4515.3303  4234.6136  7463.3809  1168.3263  2127.9401  3922.4539\n",
       " [85] 15338.5370  3636.3710  4700.7371  3738.2289  3649.2965  3075.8736\n",
       " [91]  4767.1117  7382.9251  1862.7404  1723.9324  5358.5367  3783.5527\n",
       " [97]  1631.6235  9452.3934  5725.8342  5672.2297"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rweibull(100, 1.5, 5000)"
   ]
  }
 ],
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